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Groups whose Chermak–Delgado lattice is a subgroup lattice of an abelian group

Part of: Representation theory of groups

Published online by Cambridge University Press:  17 June 2022

Lijian An Open the ORCID record for Lijian An [Opens in a new window]
Lijian An*
Affiliation:
Department of Mathematics, Shanxi Normal University, Linfen, Shanxi 041004, P. R. China
*
e-mail: anlj@sxnu.edu.cn
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Abstract

The Chermak–Delgado lattice of a finite group G is a self-dual sublattice of the subgroup lattice of G. In this paper, we prove that, for any finite abelian group A, there exists a finite group G such that the Chermak–Delgado lattice of G is a subgroup lattice of A.

Keywords

Chermak–Delgado latticesubgroup latticefinite p-groups

MSC classification

Primary: 20D30: Series and lattices of subgroups
Secondary: 20D15: Nilpotent groups, $p$-groups
Type
Article
Information
Canadian Mathematical Bulletin , Volume 66 , Issue 2 , June 2023 , pp. 443 - 449
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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Footnotes

This work was supported by NSFC (Grant No. 11971280).

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